Digital signal processing techniques performed on high-speed digital computers are utilized in many fields of technology including communications systems, test systems, defense systems and so on. Most signals of interest are analog signals, thus the conversion of a continuous analog signal to a discrete digital representation is a critical first step in any digital processing technique.
Generally, a discrete representation of an analog signal is obtained by sampling the analog signal at intervals of uniform duration, where the magnitude of the duration is T seconds.
The analog signal, f(t), may be represented as a sum of frequency components x.sub.i (t) of the form EQU f(t)=.SIGMA.x.sub.i (t)=.SIGMA.A.sub.i cos(.omega..sub.i t+.psi..sub.i)
where the quantities A.sub.i, .omega..sub.i t, and .psi..sub.i) are the amplitude, frequency, and phase of each frequency component.
If a maximum frequency, .omega..sub.max, exists so that x.sub.i (t) is zero for .omega..sub.i &gt;.omega..sub.max the signal is said to be bandlimited. For an analog signal sampled at intervals of duration T, the sampled values accurately represent the analog signal if: EQU .pi./T.ltoreq..omega..sub.max (Eq. A)
Eq. A defines the Nyquist criterion. If the Nyquist criterion is not met the sampled values will include an aliasing error due to the existence of frequency components at frequencies above .pi./T.
A more complete discussion of the aliasing problem is discussed in the book by F. G. Stremler entitled Introduction to Communication Systems, Addison-Wesley, Mass. Second Ed., 1982.
The Nyquist criterion represents a design criterion for all sampling systems. Practical limitations on equipment and of cost limit the lower range of the sampling interval T.sub.min. Thus, for test signals with .omega..sub.max &gt;.pi./T.sub.min the Nyquist criterion is violated. For these signals, pre-sampling filtering is employed to limit .omega..sub.max. Again, ideal bandlimiting is not physically possible and approximating the ideal is prohibitively expensive. Thus, existing systems utilize expensive circuitry to reduce T.sub.min and to pre-filter the test signal while not completely obviating the aliasing problem.
Accordingly, a great need exists for a practical system to generate a discrete representation of a non-bandwidth limited signal that avoids introducing an aliasing error into the sampled representation.